Magnesium under pressure: structure and phase transition

The pressure-induced martensitic transition of magnesium from the ground-state hexagonal-close-packed (hcp) structure at atmospheric pressure to a body-centred-cubic (bcc) structure at hydrostatic pressures larger than about 500 kbar is studied with the full-potential, linearized, augmented-plane-wave method. At any given value of the pressure, the minimum in the Gibbs free energy G, which gives the equilibrium structure, is found from the values of G along the epitaxial Bain path. This procedure, when repeated for several pressure values, allows the determination of the pressure dependence in the equilibrium state of the free energy, the volume per atom, the lattice parameters and the axial ratio for both the hcp and the bcc structures. The transition pressure is determined by the crossing of the free energies as functions of pressure for the hcp and bcc phases. The second strain-derivative of G at equilibrium at each pressure determines the elastic constants. For the shear constants c44 and c66 of the hcp structure, the internal relaxation of the second basis atom is taken into account. The elastic constants C' and c44 of bcc magnesium are positive and increase with pressure